Solve 3/n^2=n-4/3n^2+2/3n^25/633766

$$\frac{ 3 }{ { n }^{ 2 } } = \frac{ n-4 }{ 3 { n }^{ 2 } } + \frac{ 2 }{ 3 { n }^{ 2 } } \frac{ 5 }{ 633766 }$$

Solve for n

$$n = \frac{4119474}{316883} = 12\frac{316878}{316883} \approx 12.999984221$$

Steps for Solving Linear Equation

Variable n cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 1901298n^{2}, the least common multiple of n^{2},3n^{2},633766.

$$1901298\times 3=633766\left(n-4\right)+633766\times 2\times \frac{5}{633766}$$

Multiply 1901298 and 3 to get 5703894.

$$5703894=633766\left(n-4\right)+633766\times 2\times \frac{5}{633766}$$

Use the distributive property to multiply 633766 by n-4.

$$5703894=633766n-2535064+633766\times 2\times \frac{5}{633766}$$

Multiply 633766 and 2 to get 1267532.

$$5703894=633766n-2535064+1267532\times \frac{5}{633766}$$

Multiply 1267532 and \frac{5}{633766} to get 10.

$$5703894=633766n-2535064+10$$

Add -2535064 and 10 to get -2535054.

$$5703894=633766n-2535054$$

Swap sides so that all variable terms are on the left hand side.

$$633766n-2535054=5703894$$

Add 2535054 to both sides.

$$633766n=5703894+2535054$$

Add 5703894 and 2535054 to get 8238948.

$$633766n=8238948$$

Divide both sides by 633766.

$$n=\frac{8238948}{633766}$$

Reduce the fraction \frac{8238948}{633766} to lowest terms by extracting and canceling out 2.

$$n=\frac{4119474}{316883}$$